Properties

Label 53.a
Number of curves $1$
Conductor $53$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 53.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53.a1 53a1 \([1, -1, 1, 0, 0]\) \(3375/53\) \(-53\) \([]\) \(2\) \(-0.98855\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 53.a do not have complex multiplication.

Modular form 53.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - 3 q^{3} - q^{4} + 3 q^{6} - 4 q^{7} + 3 q^{8} + 6 q^{9} + 3 q^{12} - 3 q^{13} + 4 q^{14} - q^{16} - 3 q^{17} - 6 q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display